Question: Rewrite as a simplified fraction. ${1.1\overline{75} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1175.7575...\\ 10x &= 11.7575...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1164}$ ${x = \dfrac{1164}{990}} $ ${x = \dfrac{194}{165}} \text{or} {1 \dfrac{29}{165}}$